Several ugly rows emerged, including on the touchline between the two sets of staff. Gattuso was eventually sent off during the 3-1 win.
“Italian football has changed in its mentality for a few years now, nobody gives you anything for free," Gattuso told Sky Sport Italia.
“I deserved to be sent off today, I freely admit I went too far, a few too many words were exchanged. Unfortunately, both parties ended up taking it up a few notches and the game suffered.
“I haven't spoken to Simone Inzaghi yet, as it's better for me to wait until I've calmed down, otherwise I tend to do even more damage."
The victory was overshadowed by a late injury to Lorenzo Insigne, who was practically in tears after pulling up with pain at the top of his thigh.
“Insigne spoke to the doctor, we'll evaluate it over the next 48 hours when we have the test results. Hopefully, it's not as serious as we first thought."